Background: High costs are a limitation to scaling up the Xpert MTB/RIF assay (Xpert) for the diagnosis of tuberculosis in resource-constrained settings. A triaging strategy in which a sensitive but not necessarily highly specific rapid test is used to select patients for Xpert may result in a more affordable diagnostic algorithm. To inform the selection and development of particular diagnostics as a triage test we explored combinations of sensitivity, specificity and cost at which a hypothetical triage test will improve affordability of the Xpert assay. Methods: In a decision analytical model parameterized for Uganda, India and South Africa, we compared a diagnostic algorithm in which a cohort of patients with presumptive TB received Xpert to a triage algorithm whereby only those with a positive triage test were tested by Xpert. Findings: A triage test with sensitivity equal to Xpert, 75% specificity, and costs of US$5 per patient tested reduced total diagnostic costs by 42% in the Uganda setting, and by 34% and 39% respectively in the India and South Africa settings. When exploring triage algorithms with lower sensitivity, the use of an example triage test with 95% sensitivity relative to Xpert, 75% specificity and test costs $5 resulted in similar cost reduction, and was cost-effective by the WHO willingness-to-pay threshold compared to Xpert for all in Uganda, but not in India and South Africa. The gain in affordability of the examined triage algorithms increased with decreasing prevalence of tuberculosis among the cohort. Conclusions: A triage test strategy could potentially improve the affordability of Xpert for TB diagnosis, particularly in low-income countries and with enhanced case-finding. Tests and markers with lower accuracy than desired of a diagnostic test may fall within the ranges of sensitivity, specificity and cost required for triage tests and be developed as such.